(1)
On paper, sketch vector to some convenient scale and at the proper angle.
(2) Sketch vector to the same scale, with its tail at the head of vector a, again at
the proper angle.
(3) The vector sum
is the vector that extends from the tail of
to the head of .

we
have great freedom in choosing a coordinate system, because the relations among
vectors do not depend on the location of the origin of the coordinate system or
on the orientation of the axes. This is also true of the relations of physics;
they are all independent of the choice of coordinate system.